AP Calculus AB / Unit 6: Integration and Accumulation of Change

6.6 Applying Properties of Definite Integrals

3 practice questions

Notes

$\displaystyle \int_a^a f=0$; $\displaystyle \int_b^a f=-\int_a^b f$.
$\displaystyle \int_a^b f+\int_b^c f=\int_a^c f$.
$\displaystyle \int_a^b [kf+g]=k\int_a^b f+\int_a^b g$.
Use geometry (triangles, rectangles, semicircles) for areas.

Practice

$\displaystyle \int_1^5 f=8$ and $\displaystyle \int_1^3 f=3$. Find $\displaystyle \int_3^5 f$.

$\displaystyle \int_4^0 f(x)dx=-6$. Then $\displaystyle \int_0^4 f(x)dx=$

$\displaystyle \int_{-2}^2\sqrt{4-x^2}\,dx=$

Ready for more? Take the Unit 6 test.